I can't even begin to figure out how to answer this question, and google was very little help. So please help me if you can!

Assume annual species lives in a stochastic environment and acts in a strategy-independent way where all individuals are affected equally, and fecundity is traded off with juvenile survival. There are also some fluctuating environmental factors such as variable food supply that affects the juvenile survival so that in good years, survival is higher and the cost of fecundity is relieved. What would be the optimal life history strategy for this species? (Is this species more r or K selected or a mixture of both?).So thank you so much to anyone who can help! My first guess was possibly K selected or a mixture of both, but I'm not sure how to explain that other than in terms of juvenile survival?

I agree with basic biology here. R selection will result in the best overall fitness for such a species.

There are a number of clues in the question that help elucidate the ecology of this given species we shall call A. Now A, being an annual species, has a very short life history. Its entire life cycle will be completed in a year or less, and thus we might presume that during this time, it has to go about its business of development, maturation and reproduction. Typically such a species will be semelparous, growing throughout its life and reproducing only near the end of its life cycle, producing a large number of offspring in one bout. Naturally due to the short life cycle there is no overlap of generations, and the the only investment in each offspring is in the form of food reserves.

If this sounds familiar to you, they are the characteristics of an r-selected species: Large number of offspring, low amount of parental investment. This is the most optimal strategy for an annual species as due to the life cycle there is a) little opportunity for repeated reproduction and b) Little opportunity for parental care. All of this deduced from just the fact that A is an annual species.

Moving on, given that the environment is highly variable, it appears that investment in a small number of offspring will not be optimal, due to the risk of reproducing in bad years and losing much of the brood. Thus r selection is again better as the parent can now reproduce when conditions are temporarily favourable, producing a large brood and exploiting this environment, allowing the best chances of offspring survival, hence maximizing fitness.

Fecundity(future reproduction) vs offspring (current reproduction)

here what the costs mean is that investment in offspring costs the parent in terms of future reproduction. For example, giving extra food to an offspring in the present might reduce the parent's survival chances , and thus reduce the ability of a parent to provide food for future offspring. For more information read Life history theory. here this cost will be much smaller for A if it was r selected as although its investment in each offspring is small, the cost of reproduction is large because of the large number of offspring, however, whereas this will have hurt the ability of a K selected animal to reproduce in the future, it will not be as damaging to a r selected semelparous species because the species will have no need for future reproduction.